Fresnel integral C: Series representations (formula 06.33.06.0007)

FresnelC

$Mathematica Notation$

Gamma, Beta, Erf

FresnelC[z]

Series representations

Asymptotic series expansions

http://functions.wolfram.com/06.33.06.0007.01

Input Form

FresnelC[z] \[Proportional] (z^4)^(3/4)/(2 z^3) + (1/(Pi z)) (Sin[(Pi z^2)/2] HypergeometricPFQ[{1/4, 3/4, 1}, {}, -(16/(Pi^2 z^4))] - (1/(Pi z^2)) Cos[(Pi z^2)/2] HypergeometricPFQ[{3/4, 5/4, 1}, {}, -(16/(Pi^2 z^4))]) /; (Abs[z] -> Infinity)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2001-10-29